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No.
It depends on the eggshell genes of BOTH parents. For example:
Araucana rooster x RIR hen= daughters lay green-olive eggs, despite their mother laying only brown eggs.
RIR rooster x EE hen that lays green eggs, but genetically not pure for the green/blue eggshell gene= half of daughters lay brown or tan eggs, other half lays green-olive eggs. So half of them lay tan/brown despite their mother laying green eggs.
There are a lot of different genes for eggshell color. There are many just for the tan-brown egg pigments. A lot of the brown or tan pigments are dominant, so crosses with these strongly tend to lay tinted-brown eggshells.
Sometimes in threads concerning EE, Araucana, Amers, someone will bring up or recommend using roosters that hatched from a blue egg.. however this is not fool proof, it is largely making a "bet" the rooster is more than likely to have the blue eggshell gene in him.
Same goes for recommending Marans roosters that hatched from really dark eggs- it's the hopes he will have inherited most of the desired genes for darker eggs..
Same concept goes for hatching the 'best eggs'- the hen who laid them had the desirable combination of genes and it's the hope to hatch out chicks that have more of the desirable genes.